Nuprl Lemma : length_functionality_wrt_permr
∀A:Type. ∀as,as':A List. ((as ≡(A) as') ⇒ (||as|| = ||as'|| ∈ ℤ))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
length: ||as||,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
true: True,
all: ∀x:A. B[x],
prop: ℙ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
iabmonoid: IAbMonoid,
imon: IMonoid,
so_lambda: λ2x.t[x],
so_apply: x[s],
grp_car: |g|,
pi1: fst(t),
int_add_grp: <ℤ+>
Lemmas referenced :
permr_wf,
list_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
length_mon_for_char,
subtype_rel_self,
iff_weakening_equal,
int_add_grp_wf,
subtype_rel_sets,
grp_sig_wf,
monoid_p_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
inverse_wf,
grp_inv_wf,
comm_wf,
mem_f_wf,
mon_for_wf,
mon_for_functionality_wrt_permr
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
intEquality,
hypothesisEquality,
natural_numberEquality,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
inhabitedIsType,
isectElimination,
universeEquality,
lambdaFormation_alt,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination,
independent_functionElimination,
setEquality,
cumulativity,
setElimination,
rename,
because_Cache,
setIsType
Latex:
\mforall{}A:Type. \mforall{}as,as':A List. ((as \mequiv{}(A) as') {}\mRightarrow{} (||as|| = ||as'||))
Date html generated:
2019_10_16-PM-01_02_39
Last ObjectModification:
2018_10_08-AM-11_46_32
Theory : list_2
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