Nuprl Lemma : qadd_comm_q
∀[a,b:ℚ]. ((a + b) = (b + a) ∈ ℚ)
Proof
Definitions occuring in Statement :
qadd: r + s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
iabmonoid: IAbMonoid,
imon: IMonoid,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
infix_ap: x f y
Lemmas referenced :
abmonoid_comm,
qadd_grp_wf,
subtype_rel_sets,
grp_sig_wf,
monoid_p_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
inverse_wf,
grp_inv_wf,
comm_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
setEquality,
cumulativity,
hypothesisEquality,
setElimination,
rename,
because_Cache,
lambdaEquality_alt,
setIsType,
universeIsType,
independent_isectElimination,
lambdaFormation_alt
Latex:
\mforall{}[a,b:\mBbbQ{}]. ((a + b) = (b + a))
Date html generated:
2020_05_20-AM-09_14_09
Last ObjectModification:
2020_02_03-PM-02_58_14
Theory : rationals
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