Nuprl Lemma : test-sq-stuff
∀L,L2:ℤ List. ((L = L2 ∈ (ℤ List)) ⇒ (||L|| = ||L2|| ∈ ℤ))
Proof
Definitions occuring in Statement :
length: ||as||,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
true: True,
squash: ↓T,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_subtype_base,
int_subtype_base,
list_wf,
length_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
equalityIsType4,
inhabitedIsType,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
sqequalRule,
universeIsType,
natural_numberEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality,
because_Cache,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}L,L2:\mBbbZ{} List. ((L = L2) {}\mRightarrow{} (||L|| = ||L2||))
Date html generated:
2019_10_15-AM-11_34_02
Last ObjectModification:
2018_10_31-PM-06_00_36
Theory : general
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