Nuprl Lemma : txpose_perm_wf
∀n:ℕ. ∀i,j:ℕn. (txpose_perm(i;j) ∈ 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],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
txpose_perm: txpose_perm,
sym_grp: Sym(n),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
tidentity: Id{T},
inv_funs: InvFuns(A;B;f;g),
and: P ∧ Q
Lemmas referenced :
mk_perm_wf_a,
int_seg_wf,
swap_wf,
nat_wf,
swap_order_2
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
independent_functionElimination,
inhabitedIsType,
universeIsType,
independent_pairFormation
Latex:
\mforall{}n:\mBbbN{}. \mforall{}i,j:\mBbbN{}n. (txpose\_perm(i;j) \mmember{} Sym(n))
Date html generated:
2019_10_16-PM-00_59_20
Last ObjectModification:
2018_10_08-AM-09_26_39
Theory : perms_1
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