Nuprl Lemma : txpose_perm_inv
∀n:ℕ. ∀i,j:ℕn. (inv_perm(txpose_perm(i;j)) = txpose_perm(i;j) ∈ Sym(n))
Proof
Definitions occuring in Statement :
txpose_perm: txpose_perm,
sym_grp: Sym(n),
inv_perm: inv_perm(p),
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,
txpose_perm: txpose_perm,
inv_perm: inv_perm(p),
mk_perm: mk_perm(f;b),
perm_b: p.b,
pi2: snd(t),
perm_f: p.f,
pi1: fst(t)
Lemmas referenced :
int_seg_wf,
nat_wf,
txpose_perm_wf
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,
sqequalRule,
dependent_functionElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}i,j:\mBbbN{}n. (inv\_perm(txpose\_perm(i;j)) = txpose\_perm(i;j))
Date html generated:
2019_10_16-PM-00_59_23
Last ObjectModification:
2018_10_08-AM-09_26_37
Theory : perms_1
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