Nuprl Lemma : txpose_perm_id
∀n:ℕ. ∀i,j:ℕn. ((i = j ∈ ℤ) ⇒ (txpose_perm(i;j) = id_perm() ∈ Sym(n)))
Proof
Definitions occuring in Statement :
txpose_perm: txpose_perm,
sym_grp: Sym(n),
id_perm: id_perm(),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n,
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,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
uimplies: b supposing a,
sym_grp: Sym(n),
perm: Perm(T),
prop: ℙ,
true: True,
id_perm: id_perm(),
txpose_perm: txpose_perm,
squash: ↓T
Lemmas referenced :
istype-int,
set_subtype_base,
lelt_wf,
int_subtype_base,
int_seg_wf,
nat_wf,
inv_funs_wf,
perm_f_wf,
perm_b_wf,
swap_id,
mk_perm_wf,
squash_wf,
true_wf,
istype-universe,
txpose_perm_wf,
perm_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
equalityIsType4,
introduction,
extract_by_obid,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
lambdaEquality_alt,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
inhabitedIsType,
universeIsType,
dependent_set_memberEquality_alt,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
imageElimination,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeEquality,
imageMemberEquality,
applyLambdaEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}i,j:\mBbbN{}n. ((i = j) {}\mRightarrow{} (txpose\_perm(i;j) = id\_perm()))
Date html generated:
2019_10_16-PM-00_59_31
Last ObjectModification:
2018_10_08-AM-09_26_32
Theory : perms_1
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