Nuprl Lemma : comb_for_txpose_perm_wf
λn,i,j,z. txpose_perm(i;j) ∈ n:ℕ ⟶ i:ℕn ⟶ j:ℕn ⟶ (↓True) ⟶ Sym(n)
Proof
Definitions occuring in Statement :
txpose_perm: txpose_perm,
sym_grp: Sym(n),
int_seg: {i..j-},
nat: ℕ,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
nat: ℕ
Lemmas referenced :
txpose_perm_wf,
squash_wf,
true_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
isectElimination,
inhabitedIsType,
natural_numberEquality,
setElimination,
rename
Latex:
\mlambda{}n,i,j,z. txpose\_perm(i;j) \mmember{} n:\mBbbN{} {}\mrightarrow{} i:\mBbbN{}n {}\mrightarrow{} j:\mBbbN{}n {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} Sym(n)
Date html generated:
2019_10_16-PM-00_59_21
Last ObjectModification:
2018_10_08-AM-09_26_38
Theory : perms_1
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