Nuprl Lemma : txpose_perm_sym
∀n:ℕ. ∀i,j:ℕn. (txpose_perm(i;j) = txpose_perm(j;i) ∈ Sym(n))
Proof
Definitions occuring in Statement :
txpose_perm: txpose_perm,
sym_grp: Sym(n),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
sym_grp: Sym(n),
perm: Perm(T),
prop: ℙ,
txpose_perm: txpose_perm,
squash: ↓T,
true: True
Lemmas referenced :
int_seg_wf,
nat_wf,
inv_funs_wf,
perm_f_wf,
perm_b_wf,
mk_perm_wf,
squash_wf,
true_wf,
istype-universe,
swap_sym,
txpose_perm_wf,
perm_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
inhabitedIsType,
hypothesisEquality,
universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
dependent_set_memberEquality_alt,
because_Cache,
dependent_functionElimination,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
applyLambdaEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}i,j:\mBbbN{}n. (txpose\_perm(i;j) = txpose\_perm(j;i))
Date html generated:
2019_10_16-PM-00_59_29
Last ObjectModification:
2018_10_08-AM-09_26_34
Theory : perms_1
Home
Index